Navigating Multiple Frictions: Experimental evidence for impacting voucher take-up at scale | Abhijeet Singh

Ten minutes for your mind@2:50 every day at 2:50 pm in multiple time zones:Europa@2:50, EET, Athens, Helsinki (UTC+2) (7:50 am EST) https://us02web.zoom.us/j/88298032734Atlantica@2:50, EST, New York, Toronto (UTC-4) https://us02web.zoom.us/j/85349851047Pacifica@2:50, PST, Los Angeles, Vancouver (UTC=7) (5:50 pm EST) https://us02web.zoom.us/j/85743543699Almost everything works better again if you unplug it for a bit, including your mind. Stop by and unplug. Get the benefits of mindfulness without the fuss.@2:50 meets at the same time every single day for ten minutes of quiet together.No pre-requisite, no registration needed.Visit the website to view all @2:50 time zones each day.at250.org or at250.mit.edu

Time: 3:00 PM - 4:00 PMSpeaker: Grant Barkley (Harvard)Title: Infinite root systems in algebra and geometryAbstract: We describe how biclosed sets of roots in a positive root system simultaneously give a natural completion of the weak order on a Coxeter group and a combinatorial skeleton for Calabi-Yau categories. In particular, for affine root systems, we show that biclosed sets form a profinite semidistributive lattice, strengthening the lattice property conjectured by Dyer. We also show that each torsion class in the category of modules for an affine type A preprojective algebra has an associated biclosed set of roots, which uniquely determines the spherical modules in the torsion class; in this way biclosed sets behave like stability conditions on the category. We apply biclosed sets to give a new proof that Bruhat intervals have EL-labelings and to prove an extension of the Gelfand-Serganova theorem on Coxeter matroids to infinite Coxeter groups. We also prove new cases of the combinatorial invariance conjecture for Kazhdan-Lusztig polynomials.____________________________________________________________________________________________________Time: 4:15 PM - 5:15 PMSpeaker: Yuhan Jiang (Harvard)Title: Enumeration in stochastic processes and polyhedral geometryAbstract: This dissertation explores the combinatorics of Markov chains and polyhedral geometry, with a focus on the asymmetric simple exclusion process (ASEP) and the Ehrhart theory of polytopes. The first part addresses the stationary distribution of stochastic models, including the open ASEP, the Arndt-Heinzel-Rittenberg (AHR) model and the doubly ASEP (DASEP).We give a two-layer simple random walk interpretation for the open ASEP model, a tableaux formula for the AJR model, and show that the DASEP exhibits homomesy phenomenon.The second part of the dissertation studies the Ehrhart theory of positroid polytopes and alcoved polytopes. We present combinatorial formulas for the $h^*$-polynomials of positroid polytopes and alcoved polytopes.

Speaker: Zhihan Wang (Cornell)Title: Shape of Mean Curvature Flow Passing Through a Non-degenerate SingularityAbstract:A central question in geometric flow is to understand the change of geometry and topology after passing through singularities. In this talk, I will focus on mean curvature flow, the negative gradient flow of area functional, and explain how the local dynamics influence the shape of the flow near a singularity, as well as how the geometry and topology of the flow change after passing through a singularity with generic dynamics. This talk is based on the joint work with Ao Sun and Jinxin Xue.

Speaker: Thomas Hameister (Boston College)Title: Relative Duality for Hitchin SystemsAbstract: The Hitchin fibration for a reductive group G is a certain generalized abelian fibration, which admits remarkable duality properties. Namely, the "semi-classical limit" of geometric Langlands asserts that the Hitchin fibrations for G and for its Langlands dual Gv are generically dual abelian fibrations. In this talk, we will explore a relative form of this duality, in the sense of Ben-Zvi, Sakellaridis, and Venkatesh. We associate to a spherical variety or symplectic representation particular sheaves on the Hitchin moduli spaces for G and Gv which we conjecture to be Fourier-Mukai dual, generalizing a conjecture of Hitchin. We will show how this duality reduces to simple calculations in invariant theory, which are confirmed in many examples in our work and which have been proved in the strongly tempered case in the forthcoming work of Ben-Zvi, Sakellaridis, and Venkatesh. This is based on joint work with Zhilin Luo and Benedict Morrissey.

Title: TBD